Hello @Geoffrey! Thanks for this interesting question, and I apologize in advance for having too much fun with the owl metaphor in the following paragraphs.
With a C1 symmetric particle like an owl, I would not expect this type of motion to be modellable. To understand why, it’s useful to focus on the training step of 3D Flex rather than the reconstruction.
Recall that 3D Flex models the types of motion present in the dataset (and the deformations of each particle) by modelling the deformation of tetrahedral cells which enclose the map. By deforming the vertices of these tetrahedra, we model continuous motion (e.g., the animation in this guide section).
To deform a tetrahedron, the model must pay a cost associated with that tetrahedron’s rigidity. This penalty helps reduce overfitting. If the owl’s head was turning only slightly left and right, perhaps reading a newspaper article on local mouse populations, the costs associated with these slight deformations would be relatively small — the model could “afford” them. However, to model a full 360° rotation, the model would have to significantly deform these tetrahedra so that the head rotated from -180° – +180°.
These costs could be mitigated by creating three meshes: the owl’s body, head, and a small central mesh to which each of these is fused (the “neck”) with very low rigidity. With this mesh topology, the head and body could slip past each other without themselves having to deform. However, the neck would still have to undergo significant deformations which would likely harm the overall quality of the model.
If, however, we were modelling the rotation of a more symmetric particle (perhaps a starfish doing a pirouette), a full 360° rotation could be modeled by a 360/N rotation of the domain due to symmetry. This may be more likely to work, but I am still not aware of such a dataset!
One more consideration: 3D Flex can only move density around. It cannot create or destroy parts of the map. If you were working with a particle with true 360° rotation, it might be difficult to produce a consensus map that would give 3D Flex enough density such that it could model such rotations.
I hope that’s all helpful, and please do let me know if you have more questions! And certainly, we’d also be interested if anyone in the community is aware of any such specimens, especially if they counter my argument above 
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